In practice there is a long tradition of actuaries calculating reserve estimates according to deterministic methods without explicit reference to a stochastic model. For instance, the chain-ladder was originally a deterministic reserving method. Moreover, the actuaries often make ad hoc adjustments of the methods, for example, smoothing of the chain-ladder development factors, in order to fit the data set under analysis. However, stochastic models are needed in order to assess the variability of the claims reserve. The standard statistical approach would be to first specify a model, then find an estimate of the outstanding claims under that model, typically by maximum likelihood, and finally the model could be used to find the precision of the estimate. As a compromise between this approach and the actuary's way of working without reference to a model the object of the research area has often been to first construct a model and a method that produces the actuary's estimate and then use this model in order to assess the uncertainty of the estimate. A drawback of this approach is that the suggested models have been constructed to give a measure of the precision of the reserve estimate without the possibility of changing the estimate itself. The starting point of this thesis is the inconsistency between the deterministic approaches used in practice and the stochastic ones suggested in the literature. On one hand, the purpose of Paper I is to develop a bootstrap technique which easily enables the actuary to use other development factor methods than the pure chain-ladder relying on as few model assumptions as possible. This bootstrap technique is then extended and applied to the separation method in Paper II. On the other hand, the purpose of Paper III is to create a stochastic framework which imitates the ad hoc deterministic smoothing of chain-ladder development factors which is frequently used in practice.

It is an important step in clinical practice to discriminate real diseased patients from healthy persons. It would be great to get such discrimination from some common information like personal information, life style, and the contact with diseased patient. In this study, a score is calculated for each patient based on a survey through generalized linear model, and then the diseased status is decided according to previous sexually transmitted diseases (STDs) records. This study will facilitate clinics in grouping patients into real diseased or healthy, which in turn will affect the method clinics take to screen patients: complete screening for possible diseased patient and some common screening for potentially healthy persons.

Multivariate generalized linear mixed models (MGLMM) are used for jointly modeling the clustered mixed outcomes obtained when there are two or more responses repeatedly measured on each individual in scientific studies. The relationship among these responses is often of interest. In the clustered mixed data, the correlation could be present between repeated measurements either within the same observer or between different observers on the same subjects. This study proposes a series of in- dices, namely, intra, inter and total correlation coefficients, to measure the correlation under various circumstances of observations from a multivariate generalized linear model, especially for joint modeling of clustered count and continuous outcomes. Bayesian methods are widely used techniques for analyzing MGLMM. The need for noninformative priors arises when there is insufficient prior information on the model parameters. Another aim of this study is to propose an approximate uniform shrinkage prior for the random effect variance components in the Bayesian analysis for the MGLMM. This prior is an extension of the approximate uniform shrinkage prior. This prior is easy to apply and is shown to possess several nice properties. The methods are illustrated in terms of both a simulation study and a case example.

Cattails (Typha spp.) are invasive and tend to decrease the biodiversity and area of open water of marshes, particularly where the natural hydrological cycles have been altered, as in Delta Marsh, Manitoba. Understanding the distribution of T. latifolia L., T. angustifolia L., their hybrid, T. x glauca Godr., and the environmental variables associated with their habitats, may give valuable insight for managing cattails. The distribution of these cattail species and hybrid were surveyed in 2011 in prairie pothole and roadside ditch marshes across southwestern Manitoba and southeastern Saskatchewan. Plants were identified by analysis of microscopic leaf-lamina margin characteristics. T. x glauca was most widespread, followed by T. latifolia, whereas T. angustifolia was rare and only found as far west as central Manitoba. Current understanding of the correlations between cattail invasions and their environment is conflicting and largely based on lacustrine wetland studies. A generalized linear model was developed. The model explained approximately 40% of the variation in T. x glauca distribution in the prairie potholes and ditches. The model included the environmental variables of sediment Olsen-P, sediment nitrate-N, water pH, litter depth, surrounding land use, and the interaction between Olsen-P and nitrate-N. Olsen-P was the most important of these variables, because its removal from the model significantly reduced the residual deviance of the model (P=0.05). In a survey of 13 transects throughout Delta Marsh in 2009, hybrid cattail, T. x glauca, was dominant, T. angustifolia was rare, and T. latifolia was absent. ANOVA linear regression (P=0.05) revealed that above-ground biomass was correlated with mean cattail ramet height, cattail ramet density, and standing litter biomass. Cattail ramet density was negatively correlated with sampling date and positively correlated with standing litter biomass. Mean cattail height was correlated with fallen litter biomass. One-way ANOVA (P=0.05) revealed that fallen litter biomass was lowest in quadrats closer to the open water, and mean cattail height was greatest at the quadrats closest to the open water. While mean cattail height differed depending on whether the cattail stand was a hybrid monoculture or a mixed stand of T. x glauca and T. angustifolia, no other cattail population variables were correlated with stand type. As revealed by one-way ANOVA (P=0.05), water conductivity, sediment texture, total-N, nitrate-N, Olsen-P, and organic-C were not important variables in the distributions of T. x glauca or T. angustifolia at Delta Marsh. Therefore, managing the nutrient levels at Delta Marsh would not likely be important for limiting the distribution of the cattails at this marsh. However, reducing the P concentration in pothole and ditch marshes may limit cattails in those environments.

For well over 200 years, scientists and doctors have been poking and prodding brains in every which way in an effort to understand how they work. The earliest pokes were quite crude, often involving permanent forms of brain damage. Though neural injury continues to be an active area of research within neuroscience, technology has given neuroscientists a number of tools for stimulating and observing the brain in very subtle ways. Nonetheless, the basic experimental paradigm remains the same; poke the brain and see what happens. For example, neuroscientists studying the visual or auditory system can easily generate any image or sound they can imagine to see how an organism or neuron will respond. Since neuroscientists can now easily design more pokes then they could every deliver, a fundamental question is ``What pokes should they actually use?' The complexity of the brain means that only a small number of the pokes scientists can deliver will produce any information about the brain. One of the fundamental challenges of experimental neuroscience is finding the right stimulus parameters to produce an informative response in the system being studied. This thesis addresses this problem by developing algorithms to sequentially optimize neurophysiology experiments. Every experiment we conduct contains information about how the brain works. Before conducting the next experiment we should use what we have already learned to decide which experiment we should perform next. In particular, we should design an experiment which will reveal the most information about the brain. At a high level, neuroscientists already perform this type of sequential, optimal experimental design; for example crude experiments which knockout entire regions of the brain have given rise to modern experimental techniques which probe the responses of individual neurons using finely tuned stimuli. The goal of this thesis is to develop automated and rigorous methods for optimizing neurophysiology experiments efficiently and at a much finer time scale. In particular, we present methods for near instantaneous optimization of the stimulus being used to drive a neuron.

In traffic safety analysis, a large number of distributions have been proposed to analyze motor vehicle crashes. Among those distributions, the traditional Poisson and Negative Binomial (NB) distributions have been the most commonly used. Although the Poisson and NB models possess desirable statistical properties, their application on modeling motor vehicle crashes are associated with limitations. In practice, traffic crash data are often over-dispersed. On rare occasions, they have shown to be under-dispersed. The over-dispersed and under-dispersed data can lead to the inconsistent standard errors of parameter estimates using the traditional Poisson distribution. Although the NB has been found to be able to model over-dispersed data, it cannot handle under-dispersed data. Among those distributions proposed to handle over-dispersed and under-dispersed datasets, the Conway-Maxwell-Poisson (COM-Poisson) and double Poisson (DP) distributions are particularly noteworthy. The DP distribution and its generalized linear model (GLM) framework has seldom been investigated and applied since its first introduction 25 years ago. The objectives of this study are to: 1) examine the applicability of the DP distribution and its regression model for analyzing crash data characterized by over- and under-dispersion, and 2) compare the performances of the DP distribution and DP GLM with those of the COM-Poisson distribution and COM-Poisson GLM in terms of goodness-of-fit (GOF) and theoretical soundness. All the DP GLMs in this study were developed based on the approximate probability mass function (PMF) of the DP distribution. Based on the simulated data, it was found that the COM-Poisson distribution performed better than the DP distribution for all nine mean-dispersion scenarios and that the DP distribution worked better for high mean scenarios independent of the type of dispersion. Using two over-dispersed empirical datasets, the results demonstrated that the DP GLM fitted the over-dispersed data almost the same as the NB model and COM-Poisson GLM. With the use of the under-dispersed empirical crash data, it was found that the overall performance of the DP GLM was much better than that of the COM-Poisson GLM in handling the under-dispersed crash data. Furthermore, it was found that the mathematics to manipulate the DP GLM was much easier than for the COM-Poisson GLM and that the DP GLM always gave smaller standard errors for the estimated coefficients.

abstract: This study concerns optimal designs for experiments where responses consist of both binary and continuous variables. Many experiments in engineering, medical studies, and other fields have such mixed responses. Although in recent decades several statistical methods have been developed for jointly modeling both types of response variables, an effective way to design such experiments remains unclear. To address this void, some useful results are developed to guide the selection of optimal experimental designs in such studies. The results are mainly built upon a powerful tool called the complete class approach and a nonlinear optimization algorithm. The complete class approach was originally developed for a univariate response, but it is extended to the case of bivariate responses of mixed variable types. Consequently, the number of candidate designs are significantly reduced. An optimization algorithm is then applied to efficiently search the small class of candidate designs for the D- and A-optimal designs. Furthermore, the optimality of the obtained designs is verified by the general equivalence theorem. In the first part of the study, the focus is on a simple, first-order model. The study is expanded to a model with a quadratic polynomial predictor. The obtained designs can help to render a precise statistical inference in practice or serve as a benchmark for evaluating the quality of other designs. / Dissertation/Thesis / Doctoral Dissertation Statistics 2017

abstract: Nowadays product reliability becomes the top concern of the manufacturers and customers always prefer the products with good performances under long period. In order to estimate the lifetime of the product, accelerated life testing (ALT) is introduced because most of the products can last years even decades. Much research has been done in the ALT area and optimal design for ALT is a major topic. This dissertation consists of three main studies. First, a methodology of finding optimal design for ALT with right censoring and interval censoring have been developed and it employs the proportional hazard (PH) model and generalized linear model (GLM) to simplify the computational process. A sensitivity study is also given to show the effects brought by parameters to the designs. Second, an extended version of I-optimal design for ALT is discussed and then a dual-objective design criterion is defined and showed with several examples. Also in order to evaluate different candidate designs, several graphical tools are developed. Finally, when there are more than one models available, different model checking designs are discussed. / Dissertation/Thesis / Ph.D. Industrial Engineering 2013

A long record of daily data is used to study the lake levels of Lake Neusiedl, a large steppe lake at the eastern border of Austria. Daily lake level changes are modeled as functions of precipitation, temperature, and wind conditions. The occurrence and the amount of daily precipitation are modeled with logistic regressions and generalized linear models.

This thesis is intent on using mixtures of probability distributions in generalized linear model. The theoretical part is divided into two parts. In the first chapter a generalized linear model (GLM) is defined as an alternative to the classical linear regression model. The second chapter describes the mixture of probability distributions and estimate of their parameters. At the end of the second chapter, the previous theories are connected into the finite mixture generalized linear model. The last third part is practical and shows concrete examples of these models.